2. Solve the initial value problems using separation of variables. a. x' = t²x² , x(0) = 1 x(t) = t b. x' = хех x(1) = 0

5. The accumulated average price in millions of dollars of a two-bedroom apartment in downtown New York City from 1990 to 2010 could be approximated by P(t) = = 0.63e0.25t, where t is time in years since 1990. a) Determine P(6) and interpret your answer in context of the problem. b) Determine P'(6) and interpret your answer in context of the problem c) Determine P"(6) and interpret your answer in context of the problem.

5. Find the first derivative of x² + 3xy + y³ = 10 implicitly.

8. Solve (a) y' = (3y²)-1 (Hint: Separate.)

16. Solve (1 +x)y' xy